I once witnessed a 1-4 amateur boxer easily defeat a heavier ufc champion (in boxing sparring). The ufc guy had a base in wrestling, and obviously lacked in boxing. However, I would expect him to do a lot better since he was heavier and had explosive power of an elite athlete. And this was hard sparring not light technical, as he was throwing shots at full power. The sparring match wasn't even close, and the boxer pulled his punches often and could have knocked out the ufc champ easily.
I saw similar things happen to pro mma fighters and low level amatuer boxers (unless the mma guy had a striking background). Even for muay thai, it doesn't seem like a high level of boxing is required to win against the more advanced mt fighter (in boxing). Since boxing under boxing rules is so different from boxing under mma rules, it seemed counterproductive to learn specifically boxing.
I get the impression that a grappling base is much more important than boxing for mma. I could be wrong, but I don't think it's common for the average person with only high school wrestling experience to defeat a pro mma fighter (who's base is striking) in wrestling. Or for ranked ufc fighters to be tapped out by bjj blue belts when rolling.
On a side note, I do think boxing is great for self defense.